Excitons and biexcitons in symmetric electron-hole bilayers

Abstract

Symmetric electron-hole bilayer systems have been studied at zero temperature using the diffusion quantum Monte Carlo method. A flexible trial wave function is used that can describe fluid, excitonic and biexcitonic phases. We calculate condensate fractions and pair correlation functions for a large number of densities rs and layer separations d. At small d we find a one-component fluid phase, an excitonic fluid phase, and a biexcitonic fluid phase, and the transitions among them appear to be continuous. At d = 0, excitons appear to survive down to about rs = 0.5 a.u., and biexcitons form at rs > 2.5 a.u. [4] These systems are expected to exhibit rich phase diagrams with Fermi fluid, excitonic superfluid, biexcitonic, and charge density wave phases. [5][6][7] We have studied the simplest possible such model system, with equal electron and hole populations and equal masses, and parallel infinitely-thin twodimensional layers of variable separation and carrier density. It is important to establish the behavior of this simple system before more complicated cases such as those of unequal electron and hole masses [8] and/or unequal electron and hole densities [9] can be tackled with confidence. Further work will be required to study more realistic systems with anisotropic masses, finite well widths and depths, interface roughness, etc. We consider paramagnetic, symmetric, electron-hole bilayers consisting of N up-and down-spin electrons and holes of equal masses, m e = m h , where the distance between the two parallel layers is d. Hartree atomic units are used throughout ( = |e| = m e = 4πǫ 0 = 1). The Hamiltonian of the infinite system iŝwhere e i and h j are the in-plane position vectors of the ith electron and the jth hole. We use finite simulation cells subject to periodic boundary conditions, and the Coulomb sums are evaluated using two-dimensional Ewald sums.[13] Our results have been obtained with N = 29 particles of each type, giving a total of 116 particles, although we have also simulated the system with N = 57, corresponding to 228 particles, to investigate finite size effects, which we find to be small. The parameters that define the system are d and the in-layer density parameter r s = a/ √ 2πN , where a is the side of the square simulation cell. The d parameter controls the interaction between layers, while r s controls the interaction within the layers. In this paper we focus on the density range r s < 10 a.u., and we have not considered the very low density regime within which Wigner crystallization is favorable. [5,6] At large d the electron and hole layers become decoupled and the results for each layer tend towards those for the two-dimensional electron gas, [14][15][16] and when inter-layer and intra-layer interactions become comparable, i.e., at d r s , a paired phase is expected. It has been shown that biexciton formation is energetically favorable at low densities when d < 0.38 a.u. [17,18] Biexciton formation is expected to be suppressed at high densities, and this has been estimated to occur f...

High-temperature superfluidity with indirect excitons in van der Waals heterostructures

“…At this transition the excitons dissociate owing to screening and phase space filling 1 . The latest estimates 12 of the T ¼ 0 Mott transition at d ¼ 2.8a e give r s E6, which corresponds to equation (3). Interestingly, a Bardeen-Cooper-Schrieffer-like excitonic state of a dense electron-hole gas predicted by the earlier theory 37 was not found in the cited Monte-Carlo calculations 10,12 .…”

“…4. Although those simulations were done for electron-hole bilayers in vacuum, an approximate correspondence with our dielectric environment can be achieved if we neglect the correction term in the parenthesis in equation (12). The mapping is then obtained by setting the distance between the layers to d ¼ k 1 c and including the effective dielectric function E 1 in the definition of the electron Bohr radius:…”

“…Such phases include electron-hole Fermi gas, exciton Bose gas and exciton solid. The approximate phase boundaries based on available Monte-Carlo calculations [10][11][12]35,36 are shown in Fig. 4.…”

“…3 was constructed following the example of the Monte-Carlo simulations [10][11][12] in which only exciton phases with two possible spin flavours were considered. In TMDs, spin and orbital degeneracies of indirect excitons may have a more intriguing structure.…”

Spatially indirect exciton condensate phases in double bilayer graphene

“…It does not however account for the metallic Fermi liquid (FL) phase generally expected 31,59 at high exciton densities. The FL phase, like the exciton condensate, has charge transfer between bilayers, but does not support broken symmetries of charge-excitation gaps.…”